{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from math import sqrt, atan2, pi, cos, sin\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "# atan2返回对应向量的弧度值"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "from abc import ABC, abstractmethod\n",
    "\n",
    "class Expression(ABC):\n",
    "    @abstractmethod\n",
    "    def evaluate(self, **bindings):\n",
    "        pass"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "class Power(Expression):\n",
    "    def __init__(self,base,exponent):\n",
    "        self.base = base\n",
    "        self.exponent = exponent\n",
    "    def evaluate(self, **bindings):\n",
    "        return self.base.evaluate(**bindings) ** self.exponent.evaluate(**bindings)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [],
   "source": [
    "def vector_add(*v):  \n",
    "    # 向量加法(不限维度)\n",
    "    return tuple(map(sum, zip(*v)))\n",
    "\n",
    "def vector_scale(a, v):\n",
    "    # 标量乘法（不限维度）\n",
    "    return tuple(a* i for i in v)\n",
    "\n",
    "def change_C(n):\n",
    "    # 将度数转换为弧度制\n",
    "    return n*(pi/180)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 旋转二维向量\n",
    "# 1:求出向量长度\n",
    "def length(v):\n",
    "    # 求出向量的模（不限维度）\n",
    "    return sqrt(sum([i**2 for i in v]))\n",
    "\n",
    "# 2:将向量转入极坐标\n",
    "def to_polar(v):\n",
    "    # 将笛卡尔坐标转换为极坐标（二维）\n",
    "    x = v[0]\n",
    "    y = v[1]\n",
    "    return (length(v), atan2(y, x))\n",
    "\n",
    "# 3:旋转向量并以笛卡尔坐标的形式输出\n",
    "def to_cartesian(v):\n",
    "    # 将极坐标转换为笛卡尔坐标（二维）\n",
    "    l = v[0]\n",
    "    a = v[1]\n",
    "    return (l*cos(a), l*sin(a))\n",
    "\n",
    "def rotate2d(v, angle):\n",
    "    # 旋转二维向量\n",
    "    l, a = to_polar(v)\n",
    "    return to_cartesian((l, a+angle))\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "def distance(s1, s2):\n",
    "    # 求线段的长度\n",
    "    x1, y1 = s1\n",
    "    x2, y2 = s2\n",
    "    return sqrt((x1-x2)**2+(y1-y2)**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "def standard_form(u, v):\n",
    "    # 求直线的标准方程（二维）\n",
    "    x1, y1 = u\n",
    "    x2, y2 = v\n",
    "    return y2-y1, x1-x2, x1*y2-x2*y1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "def intersection(u1, u2, v1, v2):\n",
    "    # 求两直线的交点（二维）\n",
    "    a1, b1, c1 = standard_form(u1, u2)\n",
    "    a2, b2, c2 = standard_form(v1, v2)\n",
    "    m = np.array(((a1, b1),(a2, b2)))\n",
    "    c = np.array((c1, c2))\n",
    "    return np.linalg.solve(m, c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "def do_segments_intersect(s1, s2):\n",
    "    # 判断两直线的交点是否同时在两直线上的线段上(两线段是否相交)\n",
    "    u1, u2 = s1\n",
    "    v1, v2 = s2\n",
    "    d1 = distance(u1, u2)\n",
    "    d2 = distance(v1, v2)\n",
    "    try:\n",
    "        t = intersection(u1, u2, v1, v2)\n",
    "        return (distance(t, u1) <= d1 and distance(t, u2) <= d1 and distance(t, v1) <= d2 and distance(t, v2) <= d2)\n",
    "    except np.linalg.LinAlgError:\n",
    "        return False"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "True"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "def does_collide(a, b):\n",
    "    # 检测两个多边形是否有线段相交\n",
    "    \n",
    "    # 1.封装线段\n",
    "    num_1 = 0\n",
    "    num_2 = 0\n",
    "    l_1 = []\n",
    "    l_2 = []\n",
    "    for _ in range(0, len(a)):\n",
    "        l_1.append(a[num_1:num_1+2])\n",
    "        num_1 += 1\n",
    "        if num_1 == len(a)-1:\n",
    "            l_1.append([a[0], a[len(a)-1]])\n",
    "            break\n",
    "            \n",
    "    for _ in range(0, len(b)):\n",
    "        l_2.append(b[num_2:num_2+2])\n",
    "        num_2 += 1\n",
    "        if num_2 == len(b)-1:\n",
    "            l_2.append([b[0], b[len(b)-1]])\n",
    "            break\n",
    "            \n",
    "    # 检测相交\n",
    "    for i in l_1:\n",
    "        for t in l_2:\n",
    "            if do_segments_intersect(i, t):\n",
    "                return True\n",
    "            \n",
    "    return False\n",
    "    \n",
    "a = [(0, 0), (3, 0), (3, 3), (0, 3)]\n",
    "b = [(1, 1), (4, 1), (4, 4), (1, 4)]\n",
    "\n",
    "\n",
    "does_collide(a, b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [],
   "source": [
    "def Pinmian(s1, s2, s3):\n",
    "    # 传入三个点，求出其确定的平面      \n",
    "    a1, b1, c1 = s1\n",
    "    a2, b2, c2 = s2\n",
    "    a3, b3, c3 = s3\n",
    "    A = (b3-b1)*(c3-c2) - (c3-c1)*(b3-b2)\n",
    "    B = (c3-c1)*(a3-a2) - (a3-a1)*(c3-c2)\n",
    "    C = (a3-a1)*(b3-b2) - (b3-b1)*(a3-a2)\n",
    "    D = a1*A + b1*B + c1*C\n",
    "    return A, B, C, D"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "def qiudao(f, t1, t2):\n",
    "    # 求函数的平均变化率\n",
    "    return (f(t2)-f(t1))/(t2-t1)\n",
    "\n",
    "def instantaneous_rate(f, x, d=6):\n",
    "    # 求指定函数的某点的导数,精确到小数点后六位\n",
    "    stander = 10**(-6)\n",
    "    h = 1\n",
    "    ret = qiudao(f, x-h, x+h)\n",
    "    for _ in range(0, 2*d):\n",
    "        h = h / 10 \n",
    "        next_ret = qiudao(f, x-h, x+h)\n",
    "        if abs(next_ret - ret) < stander:\n",
    "            return round(next_ret, d)\n",
    "        \n",
    "        else:\n",
    "            ret = next_ret\n",
    "    raise Exception(\"Not\")\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "300.0\n"
     ]
    }
   ],
   "source": [
    "def get_oringe_fun(f):\n",
    "    # 接受一个函数并返回其导函数\n",
    "    def rate_fun(x):\n",
    "        return instantaneous_rate(f, x)\n",
    "    return rate_fun\n",
    "\n",
    "rate = get_oringe_fun(fun1)\n",
    "print(rate(10))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "0.33328333499999957\n"
     ]
    }
   ],
   "source": [
    "def small_change(f, x, dx):\n",
    "    return f(x) * dx\n",
    "\n",
    "def sqrt(x):\n",
    "    return x**2\n",
    "\n",
    "def ss(x):\n",
    "    return x**3/3\n",
    "\n",
    "def change(f, x1, x2, dx):\n",
    "    # 定积分\n",
    "    return sum(small_change(f, x, dx) for x in np.arange(x1, x2, dx))\n",
    "\n",
    "def approximate_change(f, v0, dt, T):\n",
    "    return v0 + change(f, 0, T, dt)\n",
    "\n",
    "def approximate_function(f, v0, dt):\n",
    "    # 从导函数积分出其原函数\n",
    "    def new_function(T):\n",
    "        return approximate_change(f, v0, dt, T)\n",
    "    \n",
    "    return new_function\n",
    "\n",
    "a = approximate_function(sqrt, 0, 0.0001)\n",
    "print(a(1))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x255c5a67c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "def interval_rates(f, t1, t2, dt):\n",
    "    # 返回对应间隔的平均值\n",
    "    return [(t, qiudao(f, t, t+dt)) for t in np.arange(t1, t2, dt)]\n",
    "\n",
    "def plot_interval_flow_rates(f, t1, t2, dt):\n",
    "    # 将对应间隔的平均值绘制成图\n",
    "    a = interval_rates(f, t1, t2, dt)\n",
    "    x = [i for (i,_) in a]\n",
    "    y = [i for (_,i) in a]\n",
    "    plt.scatter(x, y)\n",
    "    \n",
    "\n",
    "plot_interval_flow_rates(fun1, 1, 10, 0.3)\n",
    "\n",
    "x = np.linspace(1, 10, 100)\n",
    "y = fun2(x)\n",
    "plt.plot(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "def eulers_method(s0, v0, a, all_time, step):\n",
    "    # 使用欧拉方法进行积分\n",
    "    l = [s0]\n",
    "    s = s0\n",
    "    v = v0\n",
    "    dt = all_time/step\n",
    "    for _ in range(0, step):\n",
    "        s = vector_add(s, vector_scale(dt, v))\n",
    "        v = vector_add(v, vector_scale(dt, a))\n",
    "        l.append(s)\n",
    "        \n",
    "    return l\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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      "text/plain": [
       "<matplotlib.figure.Figure at 0x29c6c5d2b70>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 对抛物线进行模拟\n",
    "a = (0, -9.81)\n",
    "s0 = (0, 1.5)\n",
    "v0 = (30*cos(change_C(20)), 30*sin(change_C(20)))\n",
    "v1 = (30*cos(change_C(30)), 30*sin(change_C(30)))\n",
    "v2 = (30*cos(change_C(45)), 30*sin(change_C(45)))\n",
    "\n",
    "l = eulers_method(s0, v0, a, 2.2, 1000)\n",
    "\n",
    "x = [i for i,_ in l]\n",
    "y = [i for _,i in l]\n",
    "\n",
    "plt.figure(figsize=(20, 10), dpi=80)\n",
    "\n",
    "plt.plot(x, y)\n",
    "plt.grid()\n",
    "\n",
    "plt.yticks(range(10))\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x29c6dbe22e8>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "l1 = eulers_method((0, 0), v0, a, 5, 100)\n",
    "l2 = eulers_method((0, 0), v1, a, 5, 100)\n",
    "l3 = eulers_method((0, 0), v2, a, 5, 100)\n",
    "\n",
    "x1 = [i for i,_ in l1]\n",
    "y1 = [i for _,i in l1]\n",
    "\n",
    "x2 = [i for i,_ in l2]\n",
    "y2 = [i for _,i in l2]\n",
    "\n",
    "x3 = [i for i,_ in l3]\n",
    "y3 = [i for _,i in l3]\n",
    "    \n",
    "plt.figure(figsize=(20, 10), dpi=80)\n",
    "\n",
    "plt.plot(x1, y1, label=20)\n",
    "plt.plot(x2, y2, label=30)\n",
    "plt.plot(x3, y3, label=45)\n",
    "\n",
    "plt.legend()\n",
    "plt.grid()\n",
    "\n",
    "\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n",
      "2\n",
      "3\n",
      "3.114324\n"
     ]
    }
   ],
   "source": [
    "l = [(1, 2), (2, 3)]\n",
    "for (t, a) in l:\n",
    "    print(t)\n",
    "    \n",
    "print(abs(-3))  # 返回指定数的绝对值\n",
    "print(round(3.114324, 6))       # 对指定数进行四舍五入，可指定位数"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(3, 3, 3, 9)\n"
     ]
    }
   ],
   "source": [
    "a = (1, 1, 1)\n",
    "b = (3, 0, 0)\n",
    "c = (0, 3, 0)\n",
    "print(Pinmian(a, b, c))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "a = (1, 2, 3)\n",
    "c, d, e = a\n",
    "print(c)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([-0.22222222,  6.44444444])"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "matrix = np.array(((2, 1), (40, 2)))   # 矩阵\n",
    "output = np.array((6, 4))  # 输出向量\n",
    "np.linalg.solve(matrix, output)  # 可以求出输入向量"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "(1, -1, 0)\n",
      "[1.92307692 2.92307692]\n"
     ]
    }
   ],
   "source": [
    "print(standard_form((1, 1), (2, 2)))\n",
    "print(intersection((1, 2),(2, 3), (13, 2), (1, 3)))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1\n"
     ]
    }
   ],
   "source": [
    "a = (1, 2)\n",
    "b, c = a\n",
    "print(b)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.6.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2
}
